Monday |
Wednesday |
Friday |
8-29-11 Web
page .. PDF .. Word
Harmonic approximation for stable equilibrium, equipartition
theorem |
8-31-11 Web
page .. PDF .. Word
Solving the DEQ for simple harmonic oscillation, dot notation for derivatives, inductors |
9-2-11 Web
page .. PDF .. Word
LC Oscillators, complex representation for simple harmonic motion, Euler's theorem, commutation relations for Re, complex version of the DEQ, review of complex numbers |
| Labor Day |
9-7-11 Web
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Complex representation for AC circuits, impedance of a capacitor |
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9-12-11 Web
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The wave function, probability density, Schrodinger's equation, principle of superposition, wavenumber, quantum dispersion relation |
9-14-11 Web
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Position-wavenumber uncertainty relation, energy-time uncertainty relation, pendula, viscous damping |
9-16-11 Web
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Damped oscillators, the quality factor Q
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9-19-11 Web
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Decay of energy, damped electrical oscillator, begin driven oscillator
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9-21-11 Web
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Amplitude and phase for driven oscillator |
9-23-11 Web
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Power resonance, superposing drive forces |
9-26-11 Web
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Review for exam 1, transients |
9-28-11 Web
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Response to a triangle wave drive
annotated Mathematica notebook |
9-30-11 Web
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Driven electrical oscillator, beats, DEQs for symmetric coupled pendula |
10-3-11 Web
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Pendulum mode, breathing mode, definition of normal mode |
10-5-11 Web
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Superposing normal modes yields beats!, Hilbert space, column matrix notation for Hilbert space vectors, kets |
10-7-11 Web
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Inner products, general case of superposed normal modes |
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Fall Break |
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10-17-11 Web
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Non-zero inital velocities, analogy with molecular orbitals |
10-19-11 Web
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Damped, driven coupled oscillators |
10-21-11 Web
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Matrix multiplication, determinants, the eigenvalue equation for multiple coupled oscillators |
10-24-11 Web
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Procedure for solving the eigenvalue equation |
10-26-11 Web
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Finding eigenvectors and eigenvalues with Mathematica, orthonormality, normal mode analysis for multi-object systems |
10-28-11 Web
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The beaded string, standing wave guess |
10-31-11 Web
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Boundary conditions quantize the frequencies, Number of normal modes and minimum meaningful wavelength for the beaded string, begin example of normal mode analysis for the beaded string |
11-2-11 Web
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Example of normal mode analysis for the beaded string, including animation in Mathematica
Mathematica notebook |
11-4-11 Web
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Longitudinal oscillations, begin continuous string
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11-7-11
Review session for exam 2
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11-9-11 Web
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Inner products for continuous systems, normalized eigenvectors for the continuous string, example of normal mode analysis for the continuous string, including animation in Mathematica
Mathematica notebook |
11-11-11 Web
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k-space, basis functions, generic orthogonal function analysis, Fourier analysis |
11-14-11 Web
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Example of Fourier analysis: the sawtooth, Fourier analysis for functions of time, begin complex version of Fourier analysis
Mathematica notebook |
11-16-11 Web
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Complex version of Fourier analysis, cosine with phase version of Fourier analysis, begin experimental Fourier analysis |
11-18-11 Web
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Experimental Fourier analysis: frequency resolution, Nyquist limit, aliasing, order of frequencies in the Discrete Fourier Transform |
11-21-11 Web
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Windowing, Fourier transforms |
11-23-11 Web
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Fourier transform of a Gaussian, The Wave Equation |
Thanksgiving break |
11-28-11 Web
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E = cB, Poynting vector, superposition principle for traveling waves, non-linear waves, traveling sinusoidal waves |
11-30-11 Web
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Waves on transmission lines |
12-2-11 Web
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RMS amplitudes, begin group velocity |
12-5-11 Web
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Finish group velocity, superposing traveling waves to make standing waves |
12-7-11 Web
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Reflection and transmission of waves at interfaces |
12-9-11 Web
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Meaning of characteristic impedance of a transmission line, suppressing reflections, Snell's Law |